[2] Gordina is the daughter of mathematician Mikhail (Misha) Gordin.

[4] She completed her doctorate in 1998 from Cornell University; her dissertation, Holomorphic functions and the heat kernel measure on an infinite dimensional complex orthogonal group, was supervised by Leonard Gross.

She was awarded a National Science Foundation postdoctoral fellowship in 2000, and conducted research at the University of California, San Diego.

[8] Gordina was awarded a Humboldt Research fellowship in 2005 (with renewals), and the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics in 2009.

She was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to stochastic and geometric analysis, infinite-dimensional analysis, and ergodicity of hypoelliptic diffusions".